Properties

Label 806.2
Level 806
Weight 2
Dimension 6629
Nonzero newspaces 30
Newforms 68
Sturm bound 80640
Trace bound 7

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Defining parameters

Level: \( N \) = \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newforms: \( 68 \)
Sturm bound: \(80640\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(806))\).

Total New Old
Modular forms 20880 6629 14251
Cusp forms 19441 6629 12812
Eisenstein series 1439 0 1439

Trace form

\( 6629q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 12q^{6} + 16q^{7} - 3q^{8} + 7q^{9} + O(q^{10}) \) \( 6629q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 12q^{6} + 16q^{7} - 3q^{8} + 7q^{9} - 12q^{10} + 12q^{11} + 4q^{12} - 21q^{13} + 24q^{15} - 5q^{16} + 24q^{17} + 9q^{18} + 4q^{19} + 12q^{20} + 20q^{21} - 24q^{22} - 12q^{23} + 12q^{24} - 77q^{25} - 3q^{26} - 132q^{27} - 64q^{28} - 108q^{29} - 96q^{30} - 97q^{31} + 3q^{32} - 96q^{33} - 114q^{34} - 120q^{35} - 89q^{36} - 128q^{37} - 72q^{38} - 66q^{39} + 18q^{40} - 36q^{41} - 36q^{42} + 24q^{43} - 12q^{44} + 84q^{45} + 24q^{46} + 48q^{47} + 12q^{48} + 47q^{49} + 39q^{50} - 108q^{51} + 13q^{52} + 30q^{53} + 48q^{54} - 24q^{55} - 68q^{57} + 36q^{58} + 24q^{59} + 24q^{60} - 72q^{61} + 27q^{62} - 176q^{63} - 3q^{64} - 102q^{65} + 48q^{66} - 8q^{67} + 48q^{68} - 132q^{69} + 72q^{70} - 48q^{71} - 9q^{72} - 14q^{73} + 36q^{74} - 164q^{75} - 16q^{76} - 192q^{77} - 102q^{78} - 92q^{79} - 48q^{80} - 125q^{81} - 96q^{82} - 360q^{83} - 80q^{84} - 162q^{85} - 156q^{86} - 120q^{87} - 84q^{88} - 222q^{89} - 246q^{90} - 66q^{91} + 24q^{92} - 340q^{93} - 96q^{94} - 264q^{95} + 12q^{96} - 166q^{97} - 285q^{98} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(806))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
806.2.a \(\chi_{806}(1, \cdot)\) 806.2.a.a 1 1
806.2.a.b 1
806.2.a.c 1
806.2.a.d 1
806.2.a.e 1
806.2.a.f 1
806.2.a.g 2
806.2.a.h 2
806.2.a.i 3
806.2.a.j 5
806.2.a.k 5
806.2.a.l 6
806.2.d \(\chi_{806}(311, \cdot)\) 806.2.d.a 2 1
806.2.d.b 2
806.2.d.c 10
806.2.d.d 22
806.2.e \(\chi_{806}(521, \cdot)\) 806.2.e.a 2 2
806.2.e.b 12
806.2.e.c 12
806.2.e.d 18
806.2.e.e 20
806.2.f \(\chi_{806}(191, \cdot)\) 806.2.f.a 38 2
806.2.f.b 38
806.2.g \(\chi_{806}(373, \cdot)\) 806.2.g.a 2 2
806.2.g.b 2
806.2.g.c 4
806.2.g.d 4
806.2.g.e 6
806.2.g.f 8
806.2.g.g 20
806.2.g.h 22
806.2.h \(\chi_{806}(87, \cdot)\) 806.2.h.a 38 2
806.2.h.b 38
806.2.i \(\chi_{806}(619, \cdot)\) 806.2.i.a 80 2
806.2.k \(\chi_{806}(157, \cdot)\) 806.2.k.a 4 4
806.2.k.b 20
806.2.k.c 28
806.2.k.d 36
806.2.k.e 40
806.2.n \(\chi_{806}(621, \cdot)\) 806.2.n.a 28 2
806.2.n.b 44
806.2.o \(\chi_{806}(335, \cdot)\) 806.2.o.a 76 2
806.2.p \(\chi_{806}(25, \cdot)\) 806.2.p.a 72 2
806.2.w \(\chi_{806}(439, \cdot)\) 806.2.w.a 76 2
806.2.x \(\chi_{806}(233, \cdot)\) 806.2.x.a 160 4
806.2.ba \(\chi_{806}(119, \cdot)\) 806.2.ba.a 152 4
806.2.be \(\chi_{806}(123, \cdot)\) 806.2.be.a 144 4
806.2.bf \(\chi_{806}(57, \cdot)\) 806.2.bf.a 144 4
806.2.bg \(\chi_{806}(37, \cdot)\) 806.2.bg.a 152 4
806.2.bi \(\chi_{806}(133, \cdot)\) 806.2.bi.a 152 8
806.2.bi.b 152
806.2.bj \(\chi_{806}(9, \cdot)\) 806.2.bj.a 152 8
806.2.bj.b 152
806.2.bk \(\chi_{806}(131, \cdot)\) 806.2.bk.a 48 8
806.2.bk.b 56
806.2.bk.c 72
806.2.bk.d 80
806.2.bl \(\chi_{806}(35, \cdot)\) 806.2.bl.a 144 8
806.2.bl.b 144
806.2.bn \(\chi_{806}(151, \cdot)\) 806.2.bn.a 320 8
806.2.bo \(\chi_{806}(49, \cdot)\) 806.2.bo.a 304 8
806.2.bv \(\chi_{806}(95, \cdot)\) 806.2.bv.a 288 8
806.2.bw \(\chi_{806}(51, \cdot)\) 806.2.bw.a 288 8
806.2.bx \(\chi_{806}(173, \cdot)\) 806.2.bx.a 304 8
806.2.cb \(\chi_{806}(137, \cdot)\) 806.2.cb.a 608 16
806.2.cc \(\chi_{806}(21, \cdot)\) 806.2.cc.a 576 16
806.2.cd \(\chi_{806}(15, \cdot)\) 806.2.cd.a 576 16
806.2.ch \(\chi_{806}(11, \cdot)\) 806.2.ch.a 608 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(806))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(806)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 2}\)